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Easiest thing to do would be for him to go to his local Social Security Administration office and request a replacement card (he needs to tell them he doesn't know his number and they'll look it up for him).

Alternatively, you could hire a private investigator and they would be able to get you the number quickly and easily. The private investigator will charge you, though, while the SSA request will be free (but it'll take a couple of weeks).